How Do You Approach Top-Down Vs. Bottoms-Up Market Sizing?

In my opinion market sizing depends on the nature of the industry and what kind of numbers are available at your disposal. The trick is to ensure you are using as less as possible assumptions. 

Let's take the fitness industry as an example. You can go with a top-down approach taking into account population then filtering by age and gender and net active population. But it is based on a whole lot of assumptions and very less number based.

Bottom-up approach would be to get the number of gyms from some chain like Gold's or planet fitness then extrapolating to get the total number of estimated gym members. Then go to installs and monthly active users (MAU) for apps like Strava for cycling, etc. Nike running club, Runtastic, etc. to build on the next segment. 

This way build up as many segments as possible and then add up the market size. The number will look far more credible. You can then identify the total addressable market from this segment which will be of most interest to your investors. You can also add if some people can shift segments, etc. and leads to a much more data backed discussion. 

So net net choose the approach which has the least assumptions and the most secondary market research.

Hope this was helpful.